Answer
True
Work Step by Step
By the definition, if a set of vectors $S$ contains a linearly independent subset $S_1$, at least one vector $(x)$ from $S_1$ can be expressed as a linear combination of other vectors from $S_1$. $S$ now can be considered as superset of $S_1$, then $S$ contains all the vectors $S_1$ contains. It's mean $x$ is also in $S$. Since $S$ in a vector space $V$ contains a linearly dependent subset, $S$ is itself a linearly dependent set.
